Important note, if you take a straw that separates into two split straws (kinda in a "Y" shape) that from a topological point of view is two holes, because one is for one of these paths, and the other is an extruded hole on the side of the first path.
In topology you can't break or mend material, but you can pull, stretch, squeeze and move it all you want. So you can move one of the split straw "legs" to the bottom of the whole straw, getting a shape similar to a "V", it would look pretty much like a pair of pants. And topologically speaking it would be exactly the same.
So...
One straight hole for your mouth all the way down to your anus. Another two are there for your nostrils, that's 3 already. The rest are for your tear ducts, which have two holes on the edge of your eye, (so four in total) which merge and then connect to your nose.
So a human, from a topological perspective, is just a seven holed doughnut. Also Vsauce made a great video about that, with pretty great animations.
Nose is two. Your butt isn’t one. Or rather, your mouth and nostrils would be the entrance and your butt is the combined exit of those three holes. If you don’t count the nostrils, you only have one hole. A hole always goes through something, otherwise it’s just a cavity. And also, holes only count from one side. Your butt and mouth are the same hole, just from different ends.
Nose is only one hole homie, runs from one nostril to the other. It takes the mouth to add a secondary orifilce. And it takes the anus to add a third orifice.
Doesn’t matter which way you turn it, the result is the same. As you count it, your first hole is nostril to nostril. I count mouth to anus as hole one and then add the left and right nostrils as secondary and tertiary orifices. Having a nose ads two holes to the total count. If you had no nose, you‘d have one hole, if you only had a nose, you’d also only have one hole.
Depends on the state of your esophagus, doesn't it? If it's closed (which it mostly is) then your mouth and nose holes go to your lung cavity. Your anus is also part of a cavity that goes through your intestines all the way up your throat and stops at your esophagus.
No, the vagina is topologically a hole, as the uterus with the Fallopian tubes has two direct openings into the abdominal cavity (another objectionable "design" choice).